Meshfree method and system for numerically simulating brittle material based on damage mechanics
Meshfree model containing a number of particles to represent a structure made of brittle material is defined. At each non-initial solution cycle of a numerical simulation using the meshfree model based on damage mechanics, the following operations are performed: (a) determining one or more damage zones in the structure from simulated structural responses obtained in immediate prior solution cycle; (b) dividing the particles into a first group representing the damage zones and a second group representing the remaining of the meshfree model; (c) applying a meshfree regularization scheme by modifying each particle's strain field of the first group with a morphing function that ensures a homogeneous jump condition along respective borders of the damage zones; and (e) obtaining simulated structural behaviors of the structure using a meshfree stabilization scheme that applies to all of the particle's strain field. Each damage zone represents a crack that can grow over time.
1. A method of obtaining numerically simulated structural behaviors of brittle material comprising:
receiving, in a computer system having a meshfree-method application module installed thereon, a meshfree model containing a plurality of particles to represent a structure made of brittle material subjected to cracks; and
conducting, with the meshfree-method application module, a numerical time-marching simulation based on damage mechanics for a plurality of solution cycles using the meshfree model, at each non-initial solution cycle, performing following operations:
a) determining one or more damage zones in the structure from simulated structural behaviors obtained in immediate prior solution cycle;
b) dividing the particles of the meshfree model into a first group representing said one or more damage zones and a second group representing remaining particles of the meshfree model;
c) applying a meshfree regularization scheme by modifying each particle's strain field of the first group with a morphing function that ensures a homogeneous jump condition along respective borders of said one or more damage zones; and
e) obtaining structural behaviors of the structure using a meshfree stabilization scheme that applies to all of the particles' strain field.
2. The method of claim 1 , wherein each of the one or more damage zones represents a crack that can grow over time.
3. The method of claim 2 , wherein said morphing function is continuous within said each of the one or more damage zones.
4. The method of claim 3 , wherein said morphing function has a zero value along each of said borders.
5. The method of claim 1 , wherein the meshfree stabilization scheme comprises a stabilization force vector to compensate results caused by zero-energy modes.
6. The method of claim 1 , further comprises assigning, with the meshfree-method application module, a domain of influence or support to each of the particles.
7. A system for obtaining numerically simulated structural behaviors of brittle material comprising:
a main memory for storing computer readable code for a meshfree-method application module configured to perform a numerical simulation based on meshfree method;
at least one processor coupled to the main memory, said at least one processor executing the computer readable code in the main memory to cause the meshfree-method application module to perform following operations:
receiving a meshfree model containing a plurality of particles to represent a structure made of brittle material subjected to cracks; and
conducting, with the meshfree-method application module, a numerical time-marching simulation based on damage mechanics for a plurality of solution cycles using the meshfree model, at each non-initial solution cycle, performing following operations:
a) determining one or more damage zones in the structure from simulated structural behaviors obtained in immediate prior solution cycle;
b) dividing the particles of the meshfree model into a first group representing said one or more damage zones and a second group representing remaining particles of the meshfree model;
c) applying a meshfree regularization scheme by modifying each particle's strain field of the first group with a morphing function that ensures a homogeneous jump condition along respective borders of said one or more damage zones; and
e) obtaining structural behaviors of the structure using a meshfree stabilization scheme that applies to all of the particles' strain field.
8. The system of claim 7 , each of the one or more damage zones represents a crack that can grow over time.
9. The system of claim 8 , wherein said morphing function is continuous within said each of the one or more damage zones.
10. The system of claim 9 , wherein said morphing function has a zero value along each of said borders.
11. The system of claim 7 , wherein the meshfree stabilization scheme comprises a stabilization force vector to compensate results caused by zero-energy modes.
12. The system of claim 7 , further comprises assigning a domain of influence or support to each of the particles.
13. A non-transitory computer readable storage medium containing instructions for obtaining numerically simulated structural behaviors of brittle material by a method comprising:
receiving, in a computer system having a meshfree-method application module installed thereon, a meshfree model containing a plurality of particles to represent a structure made of brittle material subjected to cracks; and
conducting, with the meshfree-method application module, a numerical time-marching simulation based on damage mechanics for a plurality of solution cycles using the meshfree model, at each non-initial solution cycle, performing following operations:
a) determining one or more damage zones in the structure from simulated structural behaviors obtained in immediate prior solution cycle;
b) dividing the particles of the meshfree model into a first group representing said one or more damage zones and a second group representing remaining particles of the meshfree model;
c) applying a meshfree regularization scheme by modifying each particle's strain field of the first group with a morphing function that ensures a homogeneous jump condition along respective borders of said one or more damage zones; and
e) obtaining structural behaviors of the structure using a meshfree stabilization scheme that applies to all of the particles' strain field.
14. The non-transitory computer readable storage medium of claim 13 , each of the one or more damage zones represents a crack that can grow over time.
15. The non-transitory computer readable storage medium of claim 14 , wherein said morphing function is continuous within said each of the one or more damage zones.
16. The non-transitory computer readable storage medium of claim 15 , wherein said morphing function has a zero value along each of said borders.
17. The non-transitory computer readable storage medium of claim 13 , wherein the meshfree stabilization scheme comprises a stabilization force vector to compensate results caused by zero-energy modes.
18. The non-transitory computer readable storage medium of claim 13 , further comprises assigning, with the meshfree-method application module, a domain of influence or support to each of the particles.